1. Field of the Invention
The invention relates to methods wireless digital beamforming and in particular to beamforming for a time varying fading channel.
2. Description of the Prior Art
Beamforming is a signal processing technique used with arrays of transmitters or receivers that controls the directionality of, or sensitivity to, a radiation pattern. When receiving a signal, beamforming can increase the gain in the direction of wanted signals and decrease the gain in the direction of interference and noise. When transmitting a signal, beamforming can increase the gain in the direction the signal is to be sent. This is done by creating beams and nulls in the radiation pattern. Beamforming can also be thought of as spatial filtering.
Beamforming takes advantage of interference to change the directionality of the array. When transmitting, a beamformer controls the amplitude and phase of the signal at each transmitter, in order to create a pattern of constructive and destructive interference in the wavefront. When receiving, information from different sensors is combined in such a way that the expected pattern of radiation is preferentially observed.
The signal from each antenna is amplified by a different “weight.” When that weight is negative by just the right amount, noise received by that antenna can exactly cancel out the same noise received by some other antenna, causing a “null.” This is useful to ignore noise or jammers in one particular direction, while listening for events in other directions.
Conventional beamformers use a fixed set of weightings and time-delays to combine the signals from the sensors in the array, primarily using only information about the location of the sensors in space and the wave directions of interest. In contrast, beamforming techniques, generally combine this information with properties of the signals actually received by the array, typically to improve rejection of unwanted signals from other directions. As the name indicates, an beamformer is able to automatically adapt its response to different situations.
Transmit beamforming has been widely adopted for wireless systems with multiple transmit antennas. For a block fading channel, the Grassmannian beamformer has been shown to provide the best performance for given amount of feedback. However, the original Grassmannian beamformer does not take the time domain correlation of the channel fading into consideration.
Multiple-input multiple-output (MIMO) systems offer much larger channel capacity over traditional single-input single-output (SISO) systems. Recently, many transmit-beamforming algorithms have been developed to exploit the high capacity in the MIMO systems. The transmit-beamforming schemes require certain amount of channel state information (channel state information) at the transmitter. Typically, the channel state information is conveyed from the receiver to the transmitter through a feedback link. It has been shown in the art that, even with limited feedback, a good beamforming scheme can provide significant amount of array processing gain. In a slow fading environment, the performance of the transmit beamforming algorithms is usually better than that of the open-loop algorithms (algorithms based on the space-time coding). This is because extra channel information is utilized to fine tune the transmitted signal to fit the channel situation.
When perfect channel knowledge is available at the transmitter, the conventional eigen beamformer provides the best performance. However, in a practical wireless communication system, the feedback channel is band limited. The channel state information is quantized using only a few binary bits. It is of special interest to design efficient transmit beamforming schemes that are based on finite rate feedback. In the art, a universal lower bound on the outage probability of finite feedback beamformer is established for a block fading model. It is demonstrated that the relative loss in outage performance from finite feedback case decreases exponentially with the number of feedback bits. In addition, a design criterion has been introduced for finite rate beamforming. This design criterion minimizes the maximum inner product between any two beamforming weights in the beamformer codebook, and the codebook problem is shown to be equivalent to the line packing problem in the Grassmannian manifold.
Several prior art beamformers have also been constructed based on the finite rate feedback constrain. It has been shown that beamforming codebook constructed based on the maximum receive SNR approach will result in the same Grassmannian beamforming criterion as previously known. Many beamforming codebooks have been constructed for the practical MIMO systems. Recently, the Grassmannian beamforming algorithm is further investigated and its SNR performance as well as symbol error rate have been accurately quantified for a given number of feedback bits.
The above transmit beamforming algorithms assume a block fading model, i.e., the MIMO channels fade independently from one frame to the next frame. However, in an ordinary wireless system, the actual channel coefficients exhibit strong inter-frame correlation. An efficient beamforming scheme should utilize this correlation and reduce the amount of feedback. A class of beamforming schemes that exploits the inter-frame correlation in channel fading have been previously introduced. This class of algorithms is called gradient feedback (GFB) beamforming algorithm. The gradient feedback algorithm applies several random perturbed transmission weights on top of the normal beamforming weight. Then a few feedback bits from the receiver 18 select the perturbed weight vector which provides the highest receive power. It has been shown that the weight adaptation in gradient feedback can be approximated by a coarse gradient adaptation. Furthermore, the performance of the gradient feedback scheme has been analyzed in terms of convergence and tracking of an auto-regressive dynamic fading model (AR1).